
P1X is a horizontal line. Define the leg
of the vertical line taken down from P2 to
P1X as point R.
Define the leg of the vertical line which
took down the two middle points of P1 and
C to P1X from Q and Q to R.
Set the middle point of points
P1 and C to
Q. Define the leg of the vertical
line taken
down from Q to P1X as T. 

If the point of extending line P2C in the
direction of C, and crossing P1X is set to
Z, since triangle P1P2Z is biequilateral
triangle, it leads to P1R=RZ, and line QR
is parallel to line P2Z. Therefore, angle
TRQ are 30degs. 

Coordinate X of point P2 is coordinates X
of point Q plus TR.
TR=TQ/tan30deg.
Point Q is the middle points of P1 and C,
therefore the coordinate X of P2 is as shown
on previous page. 

It is the same also about coordinate Y. 

The above was in the case of P2. Also in
P3, it is completely the same. 